[Paper Review] Right Handed Neutrino Currents in the SU(3)_LxU(1)_N Electroweak Theory

H. N. Long|arXiv (Cornell University)|Mar 9, 1996

Quantum and Classical Electrodynamics2 references3 citations

TL;DR

This paper investigates right-handed neutrino currents within the SU(3)_L × U(1)_N extended electroweak model, treating the right-handed neutrino as a quantum correction rather than a degenerate spin state to maintain consistency with low-energy data. It derives a stringent constraint on the mixing angle ϕ (−0.00285 ≤ ϕ ≤ 0.00018) from Z-boson decay and estimates a lower bound of 400 GeV for the new neutral gauge boson Z² mass, while also constraining the masses of non-Hermitian gauge bosons Y± and X⁰ via symmetry-breaking hierarchy.

ABSTRACT

A version of the $\mbox{SU(3)}_L\otimes \mbox{U(1)}_N$ electroweak theory in which there are right-handed neutrino currents is reconsidered in detail. We argue that in order to have a result consistent with low-energy one, the right-handed neutrino component must be treated as correction instead of an equivalent spin state. The data from the $Z$-decay allow us to fix the limit for $ϕ$ as $-0.00285 \leq ϕ\leq 0.00018$. From the neutrino neutral current scattering, we estimate a bound for the new neutral gauge boson $Z^2$ mass in the range of 400 GeV. A bound for the new charged and neutral (non-Hermitian) gauge bosons $Y^{\pm}, X^o$ is also obtained from symmetry-breaking hierarchy.

Motivation & Objective

• To re-express the SU(3)_L × U(1)_N electroweak theory with right-handed neutrino currents in a way consistent with low-energy phenomenology.
• To resolve inconsistencies arising from treating right-handed neutrinos as equivalent spin states by redefining them as quantum corrections.
• To constrain the mixing parameter ϕ using experimental data from Z-boson decays.
• To estimate the mass of the new neutral gauge boson Z² using neutrino neutral current scattering.
• To derive bounds on the masses of non-Hermitian gauge bosons Y± and X⁰ through symmetry-breaking hierarchy.

Proposed method

• The SU(3)_L × U(1)_N gauge theory is extended to include right-handed neutrino currents, with the right-handed component treated as a perturbative correction to the left-handed current.
• Low-energy constraints are applied by analyzing Z-boson decay data to fix the mixing angle ϕ.
• Neutrino neutral current scattering processes are used to derive a lower bound on the Z² gauge boson mass.
• Symmetry-breaking hierarchy is applied to constrain the masses of the charged and neutral non-Hermitian gauge bosons Y± and X⁰.
• Theoretical consistency is ensured by avoiding degeneracy between left- and right-handed neutrino states, treating the latter as corrections.
• Numerical bounds are derived using experimental limits and theoretical consistency conditions within the model framework.

Experimental results

Research questions

• RQ1 How can right-handed neutrino currents be consistently incorporated into the SU(3)_L × U(1)_N electroweak model without violating low-energy constraints?
• RQ2 What is the allowed range for the mixing parameter ϕ based on Z-boson decay data?
• RQ3 What lower bound can be placed on the mass of the new neutral gauge boson Z² using neutrino neutral current scattering?
• RQ4 How do symmetry-breaking hierarchies constrain the masses of the non-Hermitian gauge bosons Y± and X⁰?
• RQ5 Why is treating the right-handed neutrino as a correction rather than a degenerate state essential for consistency with experimental data?

Key findings

• The mixing parameter ϕ is constrained to the interval −0.00285 ≤ ϕ ≤ 0.00018 based on Z-boson decay data.
• The mass of the new neutral gauge boson Z² is estimated to be greater than 400 GeV from neutrino neutral current scattering.
• The non-Hermitian gauge bosons Y± and X⁰ are constrained via symmetry-breaking hierarchy, though their exact masses are not specified.
• Treating the right-handed neutrino as a correction rather than a degenerate spin state is essential for consistency with low-energy observations.
• The model remains viable within the given experimental and theoretical constraints, particularly in the context of neutral current interactions.
• The analysis supports the viability of the SU(3)_L × U(1)_N model with right-handed neutrino currents when quantum corrections are properly accounted for.